Inequality for experts only...?

Hi, I found this really tough inequality at a blog and nobody has solved it yet (including me)....Can somebody please help me with this please and if possible write a full solution??here ir is: "Show that (a^b)+(b^a) >1 , for every a,b belonging to (0,1)" Please give it a try...Thank you very... show more Hi, I found this really tough inequality at a blog and nobody has solved it yet (including me)....Can somebody please help me with this please and if possible write a full solution??here ir is:

"Show that (a^b)+(b^a) >1 , for every a,b belonging to (0,1)"

Please give it a try...Thank you very much in advance.....
Update: Could you please try to prove it formally as well......????
Thank you in advance...
Update 2: a and b do not take the value 0 or 1...
Update 3: Mo that's the idea of the excercise but can you complete the solution??
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